This is Turtle.

With what you have said here. I will say you have a restriction in the
gas flow from the meter outside to the pilot head burner. this can be
may number of things like Gas valve somewhere shut and you not know it,
Pilot adjustment screw set too low or has trash in the pilot lite
needle in the gas valve to set the flow of the gas to the pilot valve,
or even to you did not pay your gas bill last month. SO.

When you push the red button you over ride all valves and everything
that would hold the natural gas back which tells me you have a
restriction of some kind of the gas not getting to the pilot lite to
burn.

TURTLE